I'm not sure my son was even 6 yet (he may have been five) when he learned about subtraction. We started by talking about things: to illustrate 4 minus 2, you s

I'm not sure my son was even 6 yet (he may have been five) when he learned about subtraction. We started by talking about things: to illustrate 4 minus 2, you start with four marbles and remove 2 of them, leaving 2. For a couple of weeks he would ask me to subtract numbers, then he moved on to asking me to ask him numbers (and writing down simply arithmetic problems to solve). Then, one day, out of the blue, he asked with a look of incredulity in his eye: "Daddy. What is one minus TWO???" He clearly realized that he had come up with a question which had no representation in the marble-based construct. I was so proud. I sat down with him and drew a number line...and then showed him how we could extend the number line to the other side of zero. He does know about infinity now (he's 7) -- and his most recent revelation that there is no such thing as an infinite number of any physical object. Even germs. Even atoms -- no matter how tiny, an infinite number of them can't exist in the universe (which he certainly pictures as finite).